Null Controllability for Degenerate Parabolic Operators

the simplest problem in 2dn = 2⎧⎪⎨ u t − div(A(x)∇u) = χ ω (x)f (t, x) in Q Tu(x, 0) = u 0 (x)x ∈ O⎪⎩(possibly) + boundary conditions on Γσ(A(x)) = {λ 1 (x), λ 2 (x)} eigenvectors ε 1 (x), ε 2 (x){λ 1 (x) = d Γ (x) α , ε 1 (x) = −Dd Γ (x) = ν Γ (Π Γ (x)) near Γλ 2 (x) ≥ m > 0✬✩∀x ∈ Oε 2 (x) O❅■❅ x✫ε 1 (x)✠ Π Γ (x)Γ✪